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Ask The Wizard #130
Have you ever wondered why people choose to gamble, particularly in a casino setting where losses are common? It’s fascinating to consider whether this could apply to other industries. What drives this behavior? Is it the allure of gaining something for nothing? That's not entirely accurate, as most gamblers don't walk away with their winnings and often end up losing more. Could it be social interaction? Certainly, but that can also be found in other environments like restaurants. So what's the true allure? Having worked in a casino, I notice the same familiar faces daily, and many seem to derive little joy from their experience, challenging the notion that enjoyment is their purpose. In your view, what draws individuals toward the concept of losing money despite their inherent intelligence?
People typically engage in gambling either as a source of amusement or due to an overwhelming urge, so let’s examine both aspects.
For those who enjoy gambling, it often serves as a thrilling escape, something akin to the exhilarating experience of riding a roller coaster. Experienced gamblers may find this form of entertainment to be surprisingly inexpensive. While for me, gambling has become more of a routine, I initially played casual basic strategy blackjack for a year before transitioning to card counting. Under Atlantic City rules, betting $5 per hand typically results in a minimal expected loss of just 2 cents per hand, equating to about $1.20 lost per hour. That’s quite a reasonable expenditure for entertainment accompanied by complimentary beverages. Hence, players engaging in more skill-based games might argue that the cost for enjoyable entertainment is fairly low.
On the other hand, some individuals, like yourself, might not find anything enjoyable about gambling. This perspective is quite valid, as entertainment is subjective and varies from person to person; not everyone has to appreciate baseball or any other activity.
Regarding compulsive gambling, psychologists categorize gamblers into two main groups: those seeking the thrill of the game and those seeking an escape from reality. Typically, men tend to pursue the action in table games, while women often prefer the more solitary experience of slot machines and video poker. That’s my take on it, although I’ll admit my understanding of psychology comes from a single semester in high school two decades ago.
If you have a group of 30 individuals all born within the same year, what is the likelihood that at least two of them share the same birthday? Please elaborate on the mathematical reasoning behind your answer.
Envision these 30 individuals lined up. The chance that the second person does not share a birthday with the first is 364 out of 365. Continuing this logic, if we assume there was no match, the chances that the next person doesn’t share a birthday with either of the first two individuals is 363 out of 365. We continue this pattern, and the combined probability that no two individuals share a birthday is calculated as (364/365)*(363/365)*...*(346/365), resulting in approximately 29.3684%. It’s commonly inquired how many individuals are necessary for there to be a greater than 50% chance of a birthday match, and intriguingly, it turns out that with just 23 people, the odds of having at least one match climb to about 50.7297%.
As a croupier in a casino in the UK, I wanted to note that our version of Three Card Poker differs slightly from the pay tables listed on your site. Specifically, we offer payouts of 35 to 1 for a straight flush and 33 to 1 for three of a kind, along with other payouts for the remaining combinations.
The house edge of that pay table is 2.70%.
If you start with a certain number of eggs, and sell half of them plus an additional half egg each day, how many eggs did you originally have if after three days you end up with none? Keep in mind that at the end of each day, the number of eggs should remain a whole number.
Let’s denote the quantity of eggs at the start of the day as d (for day) and at the end of the day as n (for night). The relationship based on the problem presented is d/2 - ? = n. Hence, we can derive d in relation to n.
d/2 = n + ?
d= 2n + 1
So on the third day n=0, so d=1.
On the second day n=1, so d=3.
On the third day n=3, so d=7.
The answer to that question is that you began with 7 eggs.
In a game played with a single deck, what are the odds of being dealt at least one ace and one deuce out of four cards? Knowing this is valuable for the game of Omaha.
In probability 101, we learn that Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B). Hence, we can express Pr(A and B) as Pr(A) + Pr(B) - Pr(A or B). Here, we can define A as obtaining an ace and B as obtaining a deuce. The probability of getting at least one ace is expressed as Pr(at least one ace) = 1 - Pr(no aces) = 1 - combin(48,4)/combin(52,4) which equals 1 - 0.7187 = 0.2813. The same logic applies to deuces. Additionally, Pr(A or B), representing the probability of getting at least one ace or deuce, becomes 1 - combin(44,4)/combin(52,4), which is 1 - 0.501435 = 0.498565. Consequently, the odds of receiving at least one ace and one deuce arrive at approximately 0.063962. combin You raised an excellent point. The act of tipping indeed contributes to the house's advantage in table games. If you were to tip every 100 hands, it would effectively increase the house edge by 1%. Players of slots and video poker usually receive comped services and are generally treated in a more favorable manner, aspects that warrant consideration when selecting which game to invest your time in.
Due to table-game tips to dealers being "highly recommended", each hand/play costs or "loses" the player a little bit (as little as $0.50-$1.00 just to be considered ’live’ by dealers) each time. With games of low bankrolls and minimum bids (i.e. $1000 in pocket and $2 per play), the tip & house-edge would often make games like video-poker more worth while as far as returns and (possibly) comps are concerned.
[Bluejay adds: When factoring in tips, video poker tends to incur lower losses per hour compared to table games, though only minimally, whereas slot machines remain a significant drain on funds. For instance, a 99%-return $0.25 video poker game at 500 hands per hour results in expected losses of $6.25 per hour. This compares to blackjack where the hourly loss is determined by a 0.5% edge multiplied by 100 hands at $5, totaling $2.50, plus an additional $5 per hour in tips, bringing the total to $7.50 per hour. In contrast, a typical quarter slot machine usually costs more than double that amount each hour.]
What is the standard deviation for the Ante & Play bets in Three Card Poker?
I'm curious about the weight of casino poker chips. Furthermore, can you recommend the best store to buy poker chips that replicate the feel and sound of authentic casino chips as closely as possible?
1.64
The industry standard for casino poker chips is 11.5 grams. Genuine casino-quality chips are made from a clay composite material. While most poker chip sets are generally uniform in weight, the quality of materials often varies, and many feel more like plastic than the authentic chips. For those seeking the best quality, one option is to purchase a large quantity of $1 chips directly from a casino cage at face value. Should the casino alter their chip style or cease operations, the value of these chips may appreciate. However, for recreational use, there are numerous sets available on eBay, typically priced around $50 for a set of 500 chips. If you opt for generic chips, I suggest looking for true Paulson chips (as there are numerous knock-offs), as they match the quality of official casino chips. That said, since Paulson has stopped producing generic chips, pricing will likely be significantly higher. If the cost exceeds $1 per chip, as is often the case, it might be more prudent to purchase actual casino chips instead.
What are the odds of being dealt the jack of diamonds in 27 consecutive hands during a six-card game?
The chance of being dealt a jack of diamonds in a single hand is 6 out of 52. Therefore, the probability of receiving the jack of diamonds in 27 consecutive hands would be represented mathematically as (6/52).
Accurate strategies and insights are available for casino games such as blackjack, craps, and roulette, among many others.27= 1 in 20,989,713,842,161,800,000,000,000.